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MMG631 Linear and Integer Optimization with Applications, 7 5 hec

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The document outlines an exercise for students at Chalmers University of Technology and the University of Gothenburg, focusing on applied optimization using various software tools such as Matlab, AMPL/CPLEX, GLPK, and Clp. It includes instructions for solving linear programming problems, group examination details, preparation requirements, and specific exercises involving graphical solutions and modeling in AMPL. The document emphasizes familiarization with different solvers and their performance through practical applications.

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What is the difference between linear and integer optimization?

Both linear programming and integer programming are powerful optimization techniques with widespread applications in various fields. The key difference lies in how they handle decision variables linear programming allows continuous values, while integer programming restricts some or all variables to integers.

What is the difference between integer and linear optimization?

IP and LP are two types of OR models that can help you find the optimal solution for a problem that involves maximizing or minimizing a linear function of decision variables. The difference is that IP requires some or all of the decision variables to be integers, while LP allows them to be continuous.

What are the different types of integer linear optimization models?

There are three basic types of integer linear programming models-a total integer model, a 0-1 integer model, and a mixed integer model. In a total integer model, all the decision. variables are required to have integer solution values.

What is the difference between linear and nonlinear optimization?

Mixed integer (MILP or MIP) problems require only some of the variables to take integer values, whereas pure integer (ILP or IP) problems require all variables to be integer.

What is the difference between LP and ILP?

While the LP is solvable in polynomial time, ILP is NP-hard, i.e. there is no known algorithm which can solve it in polynomial time. Since the ILP solution space is not a convex set, we cannot use convex optimization techniques.